We show that physical devices that perform observation, prediction, or recollection share a mathematical structure. We call devices with that structure ``inference devices''. We present existence and impossibility results for inference devices. These results hold independent of the precise physical laws of our universe. The impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted. Alternatively, they can be viewed as a non-quantum mechanical ``uncertainty principle''. The mathematics of inference devices is related to the theory of Turing Machines (TM's), e.g., some impossibility results for inference devices are related to the Halting theorem for TM's. Furthermore, one can define an analog of Universal TM's (UTM's) for inference devices, which we call ``strong inference devices''. We use strong inference devices to define the ``inference complexity'' of an inference task, which is analogous to the Kolmogorov complexity of a string. A task-independent bound is derived on the difference in inference complexity of an inference task performed with two different inference devices. This is analogous to the ``encoding'' bound on the difference in Kolmogorov complexity of a string between two UTM's. However whereas the Kolmogorov complexity of a string is arbitrary up to specification of the UTM, there is no such arbitrariness in the inference complexity of an inference task. We informally discuss philosophical implications of these results, e.g., for whether the universe ``is'' a TM. We also derive some graph-theoretic properties governing sets of multiple inference devices. Next we extend the framework to address physical devices used for control, and then to address probabilistic inference.
Monday, August 13, 2007
Limits to prediction
A paper here by David Wolpert on the idea of "inference machines" -- any physical machine that would make predictions of the future -- and the inherent limits to their abilities. The abstract:
Predicting crime
Some information in predicting crime. There are a several interesting areas:
1) Predicting changes in overall crime rates (say within a nation or community). The two major factors useful for doing so are either demographic or economic, as indicated in this article from the Canadian Justice Department. The key demographic factor is the number of male between 15-25; crime rates also correlate with economic conditions (although there seems to be sme ambiguity as to whether the link is positive or negative, which makes me wonder what is really known...some argue more wealth leads to more crime ---there's more to steal -- while others say more wealth makes for less crime -- fewer people need to steal).
2) Predicting slightly more specific changes by looking for meaningful patterns. For example, there are a number of well documented seasonal cycles, as described at Crimepsychblog. For example, I quote:
3) Predicting more specific changes by treating crime in an epidemiological kind of way, realising that it has correlations in space and time. See, for example, the work of Kate Bowers, Shane Johnson and Ken Pease. Or work showing that one burglary in an area increases the chance of another crime within a few hundred yards for several months. For example:
There is, of course, also the notable work of Glaeser, Sacerdote and Scheinkman, showing that crime has significant spatial fluctuations, more than can be accounted for by economic fluctuations:
In another paper, Glaeser and Sacerdote note that crime is much more pronounced in larger than in smaller cities, although they don't go a long way to explaining why. I wonder: could this simply reflect another scaling law like those seen in many other variables such as energy consumed, the average speed of walking, etc? [I can't find the link to this at the moment, but it's the work, I think, of Geoffrey West, Luis Bettencourt and others].
A few more random observations on crime patterns:
* Another link from Crimepsychblog
to work showing that the sites where crimes are committed are not equally. Rather, they tend to be power law distributed in terms of the likelihood of crime:
The paper to see is Understanding Risky Facilities published by the US Department of Justice.
* Another interesting idea is that of Hot Products -- particular products that, in a physics sense, act as catalysts for crime. Think mobile phones or other expensive electronics stuff. A report from the UK Home Office gives more detail:
1) Predicting changes in overall crime rates (say within a nation or community). The two major factors useful for doing so are either demographic or economic, as indicated in this article from the Canadian Justice Department. The key demographic factor is the number of male between 15-25; crime rates also correlate with economic conditions (although there seems to be sme ambiguity as to whether the link is positive or negative, which makes me wonder what is really known...some argue more wealth leads to more crime ---there's more to steal -- while others say more wealth makes for less crime -- fewer people need to steal).
2) Predicting slightly more specific changes by looking for meaningful patterns. For example, there are a number of well documented seasonal cycles, as described at Crimepsychblog. For example, I quote:
Peaks in the summer months and troughs in the winter months: […Two sexual] offences follow very similar seasonal patterns to each other with a large peak in July, when indecent assault on a female is 21 per cent above trend and rape of a female is 14 per cent above trend. Theft of a pedal cycle has a very clear seasonal pattern; peaks start in May and continue to reach 29 per cent above trend in September… Arson, unlike other criminal damage offences, shows rises in summer months…
Peaks in the winter and troughs in the summer months: Just four crime types display seasonal peaks in the winter and falls in the summer. These are
all property crimes. Domestic burglary peaks to 11 per cent above trend in January. … It is important to note that domestic burglary has an opposite seasonal pattern to nondomestic burglary.
3) Predicting more specific changes by treating crime in an epidemiological kind of way, realising that it has correlations in space and time. See, for example, the work of Kate Bowers, Shane Johnson and Ken Pease. Or work showing that one burglary in an area increases the chance of another crime within a few hundred yards for several months. For example:
Crime Patterns of Risk: A Cross National Assessment
of Residential Burglary Victimization
Shane D. Johnson Æ Wim Bernasco Æ Kate J. Bowers Æ Henk Elffers Æ
Jerry Ratcliffe Æ George Rengert Æ Michael Townsley
Springer Science+Business Media, LLC 2007
Abstract Using epidemiological techniques for testing disease contagion, it has recently been found that in the wake of a residential burglary, the risk to nearby homes is temporarily elevated. This paper demonstrates the ubiquity of this phenomenon by analyzing space–time patterns of burglary in 10 areas, located in five different countries. While the precise patterns vary, for all areas, houses within 200 m of a burgled home were at an elevated risk of burglary for a period of at least two weeks. For three of the five countries, differences in these patterns may partly be explained by simple differences in target density. The findings inform theories of crime concentration and offender targeting strategies, and have implications for crime forecasting and crime reduction more generally.
There is, of course, also the notable work of Glaeser, Sacerdote and Scheinkman, showing that crime has significant spatial fluctuations, more than can be accounted for by economic fluctuations:
The high degree of variance of crime rates across space (and across time) is one of the oldest puzzles in the social sciences (see Quetelet (1835)). Our empirical work strongly suggests that this variance is not the result of observed or unobserved geographic attributes. This paper presents a model where social interactions create enough covariance across individuals to explain the high cross- city variance of crime rates. This model provides a natural index of social interactions which can compare the degree of social interaction across crimes, across geographic 1units and across time. Our index gives similar results for different data samples and suggests that the amount of social interactions are highest in petty crimes (such as larceny and auto theft), moderate in more serious crimes (assault, burglary and robbery) and almost negligible in murder and rape. The index of social interactions is also applied to non-criminal choices and we find that there is substantial interaction in schooling choice.
In another paper, Glaeser and Sacerdote note that crime is much more pronounced in larger than in smaller cities, although they don't go a long way to explaining why. I wonder: could this simply reflect another scaling law like those seen in many other variables such as energy consumed, the average speed of walking, etc? [I can't find the link to this at the moment, but it's the work, I think, of Geoffrey West, Luis Bettencourt and others].
A few more random observations on crime patterns:
* Another link from Crimepsychblog
to work showing that the sites where crimes are committed are not equally. Rather, they tend to be power law distributed in terms of the likelihood of crime:
This one points out the maths of crime: it is almost always a small fraction of any kind of place (convenience store, bar, etc) that accounts for most of the crimes. Which is maybe not so surprising as most everything works this way. But this is undoubtedly useful for policy, as in treating the spread of diseases.
The paper to see is Understanding Risky Facilities published by the US Department of Justice.
* Another interesting idea is that of Hot Products -- particular products that, in a physics sense, act as catalysts for crime. Think mobile phones or other expensive electronics stuff. A report from the UK Home Office gives more detail:
The mobile phone
A good example of a hot product is the mobile phone. Expansion of the mobile phone market has been rapid. The targeting of mobile phones is already a factor in increasing rates of street robbery. As mobile phone handsets incorporate internet technology mobile phone crime is likely to continue and increase. The ‘no-contract’ mobile phones are particularly attractive to criminals because: they allow greater anonymity for callers; there are loopholes in the ‘pay as you go’ mobile phone schemes that enable knowledgeable users to switch to other networks and avoid payment; the vouchers used to pay for calls can also be targeted for theft; vouchers are easy to reproduce; and, criminals have reprogrammed ‘prepaid’ mobile phones to obtain free calls (reported in Association of British Insurers 2000: 14). http://www.insurance.org.uk/ResearchInfo/
Examples of future hot products include (Association of British Insurers 2000)
The launch of Digital Television and the switch off of analogue transmissions may spark a crime epidemic in the rush to replace obsolete televisions. However, the offer of set-top boxes free of charge is likely to reduce their attractiveness to thieves.
Portable Digital Virtual Disc (DVD) players are now available weighing 900 grams and costing up to £1000.
Saturday, August 11, 2007
Don't forget the faeries
or the angels or saints or the vibes. Here's the results of another amazon search on "furtune teling":
1. Titania's Fortune Cards by Titania Hardie (Paperback - 5 Oct 2000)
2. Fortune-Telling with Playing Cards with Cards by Jonathan Dee (Paperback - Oct 2004)
3. Victorian Flower Oracle Kit: The Wit and Wisdom of JJ Grandville's Flowers Personified by Karen Mahony and Alex Ukolov (Paperback - 22 Jun 2006)
4. Daily Guidance from Your Angels: Oracle Cards by Doreen Virtue (Cards - 28 Sep 2006)
5. Ascended Masters Oracle Cards by Doreen Virtue (Cards - 26 April 2007)
6. Cosmic Ordering: Oracle Wish Cards by Stephen Richards; Karen Whitelaw Smith (Pamphlet - 7 Jul 2007)
7. I Ching or Book of Changes (Arkana) by C.G. Jung, Richard Wilhelm, and Cary F. Baynes (Paperback - 29 Jun 1989)
8. Tarot for Your Self: A Workbook for Personal Transformation by Mary K. Greer (Paperback - 31 May 2002)
9. Archangel Oracle Cards by Doreen Virtue (Cards - 30 April 2004)
10. Soul Lessons and Soul Purpose Oracle Cards: The Most Direct Path to Spiritual Peace and Personal Fulfillment by Sonia Choquette (Cards - 26 Jul 2007)
11. Goddess Guidance Oracle Cards by Doreen Virtue (Cards - Sep 2004)
12. 2012: The Year of the Mayan Prophecy by Daniel Pinchbeck (Paperback - 11 Jan 2007)
13. Magical Mermaids and Dolphins Oracle Cards (Large Card Decks) (Large Card Decks) by Doreen Virtue (Cards - 31 May 2003)
14. Trust Your Vibes Oracle Deck: A Psychic Tool Kit for Awakening Your Sixth Sense by Sonia Choquette (Cards - 1 Aug 2004)
15. Saints and Angels Oracle Cards by Doreen Virtue (Cards - 19 Jan 2006)
16. Medicine Cards by Jamie Sams and David Carson (Hardcover - 30 Nov 1999)
17. Magical Unicorns Oracle Cards by Doreen Virtue (Cards - May 2005)
18. Animal-speak by Ted Andrews (Paperback - Jan 1994)
19. Healing with the Fairies Oracle Cards: Heal Your Life with Help from the Fairies (Large Card Decks): Heal Your Life with Help from the Fairies (Large Card Decks) by Doreen Virtue (Cards - 1 Feb 2001)
20. Creating Sacred Space with Feng Shui by Karen Kingston (Paperback - 25 April 1996)
21. Seventy Eight Degrees of Wisdom by Rachel Pollack (Paperback - 17 Nov 1997)
22. The Complete I Ching: The Definitive Translation by the Taoist Master Alfred Huang by Alfred Huang (Paperback - April 2004)
23. A Complete Guide to Psychic Development by Cassandra Eason (Paperback - 30 May 2002)
24. The Faeries Oracle by Brian Froud and Jessica Macbeth (Paperback - 19 Nov 2001)
1. Titania's Fortune Cards by Titania Hardie (Paperback - 5 Oct 2000)
2. Fortune-Telling with Playing Cards with Cards by Jonathan Dee (Paperback - Oct 2004)
3. Victorian Flower Oracle Kit: The Wit and Wisdom of JJ Grandville's Flowers Personified by Karen Mahony and Alex Ukolov (Paperback - 22 Jun 2006)
4. Daily Guidance from Your Angels: Oracle Cards by Doreen Virtue (Cards - 28 Sep 2006)
5. Ascended Masters Oracle Cards by Doreen Virtue (Cards - 26 April 2007)
6. Cosmic Ordering: Oracle Wish Cards by Stephen Richards; Karen Whitelaw Smith (Pamphlet - 7 Jul 2007)
7. I Ching or Book of Changes (Arkana) by C.G. Jung, Richard Wilhelm, and Cary F. Baynes (Paperback - 29 Jun 1989)
8. Tarot for Your Self: A Workbook for Personal Transformation by Mary K. Greer (Paperback - 31 May 2002)
9. Archangel Oracle Cards by Doreen Virtue (Cards - 30 April 2004)
10. Soul Lessons and Soul Purpose Oracle Cards: The Most Direct Path to Spiritual Peace and Personal Fulfillment by Sonia Choquette (Cards - 26 Jul 2007)
11. Goddess Guidance Oracle Cards by Doreen Virtue (Cards - Sep 2004)
12. 2012: The Year of the Mayan Prophecy by Daniel Pinchbeck (Paperback - 11 Jan 2007)
13. Magical Mermaids and Dolphins Oracle Cards (Large Card Decks) (Large Card Decks) by Doreen Virtue (Cards - 31 May 2003)
14. Trust Your Vibes Oracle Deck: A Psychic Tool Kit for Awakening Your Sixth Sense by Sonia Choquette (Cards - 1 Aug 2004)
15. Saints and Angels Oracle Cards by Doreen Virtue (Cards - 19 Jan 2006)
16. Medicine Cards by Jamie Sams and David Carson (Hardcover - 30 Nov 1999)
17. Magical Unicorns Oracle Cards by Doreen Virtue (Cards - May 2005)
18. Animal-speak by Ted Andrews (Paperback - Jan 1994)
19. Healing with the Fairies Oracle Cards: Heal Your Life with Help from the Fairies (Large Card Decks): Heal Your Life with Help from the Fairies (Large Card Decks) by Doreen Virtue (Cards - 1 Feb 2001)
20. Creating Sacred Space with Feng Shui by Karen Kingston (Paperback - 25 April 1996)
21. Seventy Eight Degrees of Wisdom by Rachel Pollack (Paperback - 17 Nov 1997)
22. The Complete I Ching: The Definitive Translation by the Taoist Master Alfred Huang by Alfred Huang (Paperback - April 2004)
23. A Complete Guide to Psychic Development by Cassandra Eason (Paperback - 30 May 2002)
24. The Faeries Oracle by Brian Froud and Jessica Macbeth (Paperback - 19 Nov 2001)
Interesting book
Dreaming the Future: The Fantastic Story of Prediction (Hardcover)
by Clifford A. Pickover (Author)
Synopsis
For countless generations, people of every culture have practiced a broad range of dramatic and sometimes frightening techniques to peer into the future. In this fascinating book, acclaimed author Clifford Pickover presents a nearly exhaustive list of fortune-telling techniques, from the ominous practice of human sacrifice to reading clues on the Internet. Pickover not only explores a vast and colourful array of methods of prediction - including dreaming - he also evaluates the accuracy of some of the most astonishing prophecies made throughout history. Through insight and wit, Pickover unlocks the door of your imagination with engrossing mysteries, intriguing illustrations, and even modern patents and computer techniques. Also included is a range of practical experiments and recipes - from Stone Age to New Age. Prepare yourself for a strange but captivating ride!
by Clifford A. Pickover (Author)
Synopsis
For countless generations, people of every culture have practiced a broad range of dramatic and sometimes frightening techniques to peer into the future. In this fascinating book, acclaimed author Clifford Pickover presents a nearly exhaustive list of fortune-telling techniques, from the ominous practice of human sacrifice to reading clues on the Internet. Pickover not only explores a vast and colourful array of methods of prediction - including dreaming - he also evaluates the accuracy of some of the most astonishing prophecies made throughout history. Through insight and wit, Pickover unlocks the door of your imagination with engrossing mysteries, intriguing illustrations, and even modern patents and computer techniques. Also included is a range of practical experiments and recipes - from Stone Age to New Age. Prepare yourself for a strange but captivating ride!
Popular titles on Amazon
I did a search on Amazon.co.uk looking for "telling the future" and found the following list of books. They illustrate in a quick glance the huge industry still revolving around seeing into the future. (Notice: not a single mention of science.)
1. Nostradamus: The Complete Prophecies for the Future by Mario Reading (Hardcover - 15 Feb 2006)
2. Palm Reading for Beginners: Find the Future in the Palm of Your Hand (For Beginners) by Richard Webster (Paperback - Jun 2000)
3. Prophecy: What the Future Holds for You by Sylvia Browne and Lindsay Harrison (Paperback - 8 Feb 2007)
4. Explore Your Destiny with Runes: Reveal the Secrets of Your Future with This Ancient Divination System by Joanna Sandsmark (Paperback - 13 Oct 2006)
5. Your Future in a Coffee Cup - The Art Of Divining With Coffee Grounds: The Art of Divining with Coffee Grounds by Sahar Huneidi (Paperback - 1 April 2007)
6. Nostradamus 2003-2025: A History of the Future by Peter Loire (Paperback - 18 Aug 2003)
7. The Future Is Yours: Introducing Future Life Progression - The Dynamic Technique That Reveals Your Destiny by Anne Jirsch and Monica Cafferky (Paperback - 13 Sep 2007)
8. Scrying the Secrets of the Future: How to Use Crystals Balls, Water Fire, Wax, Mirrors, Shadows and Spirit Guides to Reveal Your Destiny by Cassandra Eason (Paperback - 31 Jan 2007)
9. Exploring Scrying: How to Divine the Future and Make the Most of It (Exploring Series) by Ambrose Hawk (Paperback - 30 Sep 2001)
10. Playing Cards: Predicting Your Future (Astrolog Complete Guides) by Hali Morag (Paperback - Sep 1998)
11. What's My Future?: 30 Different Oracles Reveal Your Potential for Health, Wealth, Fame and Love by Judy Hall (Paperback - 20 Oct 2000)
12. The Future-Telling Lady: And Other Stories by James Berry (Hardcover - Jan 1993)
13. Dreams of the Future: A Preview of the Futures That Lie Before Us by Chet B. Snow and Helen Wambach (Paperback - 10 Jan 1991)
14. Fortune Telling by Tarot Cards: A Beginner's Guide to Understanding the Future Using Tarot Cards by Sasha Fenton (Paperback - 30 May 1985)
15. Intuitive Arts on Money: Use Astrology, Tarot and Psychic Intuition to See Your Future (Intuitive Arts) by Arlene Tognetti and Katherine Gleason (Paperback - Jun 2005)
16. Candle Magick Divination: Good Luck - Good Fortune Secrets of Your Future Revealed in the Flame! by Dragonstar (Paperback - 1 May 2001)
17. Titania's Oraqle: A Unique Way to Predict Your Future by Titania Hardie and Sara Morris (Hardcover - 18 Sep 1998)
18. The Fortune Teller: Simple Ways to See Your Future by Sharina (Paperback - 28 Jun 2007)
19. How to Tell the Future by Sally Morningstar (Paperback - 25 Nov 2005)
20. The Wheel of Fortune: How to Control Your Future with Astro-Numerology by David Line and Julia Line (Paperback - 11 Aug 1988)
21. Gypsy Fortunes: Use the Magic of Romany Cards to Foretell the Future by Andy Cooke, Lady Lorelei, and Lorelei (Hardcover - Aug 2003)
22. Prophecy: What the Future Holds for You by Sylvia Browne (Paperback - 26 Aug 2004)
23. The Wisdom Well: Dip Into Your Subconcious to Fortell the Future with Cards by Ivarna Kalinkova (Hardcover - Aug 2003)
24. The Fortune Teller's Deck: Predict Your Future with Playing Cards by Jane Lyle (Misc. Supplies - 13 Oct 1999)
1. Nostradamus: The Complete Prophecies for the Future by Mario Reading (Hardcover - 15 Feb 2006)
2. Palm Reading for Beginners: Find the Future in the Palm of Your Hand (For Beginners) by Richard Webster (Paperback - Jun 2000)
3. Prophecy: What the Future Holds for You by Sylvia Browne and Lindsay Harrison (Paperback - 8 Feb 2007)
4. Explore Your Destiny with Runes: Reveal the Secrets of Your Future with This Ancient Divination System by Joanna Sandsmark (Paperback - 13 Oct 2006)
5. Your Future in a Coffee Cup - The Art Of Divining With Coffee Grounds: The Art of Divining with Coffee Grounds by Sahar Huneidi (Paperback - 1 April 2007)
6. Nostradamus 2003-2025: A History of the Future by Peter Loire (Paperback - 18 Aug 2003)
7. The Future Is Yours: Introducing Future Life Progression - The Dynamic Technique That Reveals Your Destiny by Anne Jirsch and Monica Cafferky (Paperback - 13 Sep 2007)
8. Scrying the Secrets of the Future: How to Use Crystals Balls, Water Fire, Wax, Mirrors, Shadows and Spirit Guides to Reveal Your Destiny by Cassandra Eason (Paperback - 31 Jan 2007)
9. Exploring Scrying: How to Divine the Future and Make the Most of It (Exploring Series) by Ambrose Hawk (Paperback - 30 Sep 2001)
10. Playing Cards: Predicting Your Future (Astrolog Complete Guides) by Hali Morag (Paperback - Sep 1998)
11. What's My Future?: 30 Different Oracles Reveal Your Potential for Health, Wealth, Fame and Love by Judy Hall (Paperback - 20 Oct 2000)
12. The Future-Telling Lady: And Other Stories by James Berry (Hardcover - Jan 1993)
13. Dreams of the Future: A Preview of the Futures That Lie Before Us by Chet B. Snow and Helen Wambach (Paperback - 10 Jan 1991)
14. Fortune Telling by Tarot Cards: A Beginner's Guide to Understanding the Future Using Tarot Cards by Sasha Fenton (Paperback - 30 May 1985)
15. Intuitive Arts on Money: Use Astrology, Tarot and Psychic Intuition to See Your Future (Intuitive Arts) by Arlene Tognetti and Katherine Gleason (Paperback - Jun 2005)
16. Candle Magick Divination: Good Luck - Good Fortune Secrets of Your Future Revealed in the Flame! by Dragonstar (Paperback - 1 May 2001)
17. Titania's Oraqle: A Unique Way to Predict Your Future by Titania Hardie and Sara Morris (Hardcover - 18 Sep 1998)
18. The Fortune Teller: Simple Ways to See Your Future by Sharina (Paperback - 28 Jun 2007)
19. How to Tell the Future by Sally Morningstar (Paperback - 25 Nov 2005)
20. The Wheel of Fortune: How to Control Your Future with Astro-Numerology by David Line and Julia Line (Paperback - 11 Aug 1988)
21. Gypsy Fortunes: Use the Magic of Romany Cards to Foretell the Future by Andy Cooke, Lady Lorelei, and Lorelei (Hardcover - Aug 2003)
22. Prophecy: What the Future Holds for You by Sylvia Browne (Paperback - 26 Aug 2004)
23. The Wisdom Well: Dip Into Your Subconcious to Fortell the Future with Cards by Ivarna Kalinkova (Hardcover - Aug 2003)
24. The Fortune Teller's Deck: Predict Your Future with Playing Cards by Jane Lyle (Misc. Supplies - 13 Oct 1999)
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